Trigonometry Examples

$3 (2 x - 2) - 2 x < 2 (3 + 2 x) - 8$

Step 1

Simplify $3 (2 x - 2) - 2 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 (2 x) + 3 \cdot - 2 - 2 x < 2 (3 + 2 x) - 8$

Step 1.1.2

Multiply $2$ by $3$ .

$6 x + 3 \cdot - 2 - 2 x < 2 (3 + 2 x) - 8$

Step 1.1.3

Multiply $3$ by $- 2$ .

$6 x - 6 - 2 x < 2 (3 + 2 x) - 8$

Step 1.2

Subtract $2 x$ from $6 x$ .

$4 x - 6 < 2 (3 + 2 x) - 8$

Step 2

Simplify $2 (3 + 2 x) - 8$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$4 x - 6 < 2 \cdot 3 + 2 (2 x) - 8$

Step 2.1.2

Multiply $2$ by $3$ .

$4 x - 6 < 6 + 2 (2 x) - 8$

Step 2.1.3

Multiply $2$ by $2$ .

$4 x - 6 < 6 + 4 x - 8$

Step 2.2

Subtract $8$ from $6$ .

$4 x - 6 < 4 x - 2$

Step 3

Move all terms containing $x$ to the left side of the inequality.

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Step 3.1

Subtract $4 x$ from both sides of the inequality.

$4 x - 6 - 4 x < - 2$

Step 3.2

Combine the opposite terms in $4 x - 6 - 4 x$ .

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Step 3.2.1

Subtract $4 x$ from $4 x$ .

$0 - 6 < - 2$

Step 3.2.2

Subtract $6$ from $0$ .

$- 6 < - 2$

Step 4

Since $- 6 < - 2$ , the inequality will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$